Question 1

Determine whether the equation defines y as a function of x.
-$$x = y ^ { 2 }$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

For a given value of $x$, there can be two values of $y$ (one positive and one negative) since $y^2 = x$. This violates the definition of a function, which requires each input to have exactly one output.

Question 2

Evaluate the function at the given value of the independent variable and simplify.
-$f ( x ) = x ^ { 2 } - 3 ; \quad f ( x - 4 )$
A) $x ^ { 2 } - 8 x + 13$
B) $x ^ { 2 } - 7$
C) $x ^ { 2 } + 16$
D) $x ^ { 2 } - 8 x + 16$

Accepted Answer

To find $f(x-4)$, substitute $x-4$ for $x$ in the function $f(x) = x^2 - 3$, resulting in $(x-4)^2 - 3$. Expanding $(x-4)^2$ gives $x^2 - 8x + 16$, and subtracting 3 gives $x^2 - 8x + 13$.

Question 3

Determine whether the equation defines y as a function of x.
-$$x + y ^ { 3 } = 27$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

The answer of Determine whether the equation defines y as...

Question 4

Determine whether the equation defines y as a function of x.
-$$y = - \sqrt { x - 9 }$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

For each value of $x$ greater than or equal to 9, there is exactly one corresponding value of $y$, satisfying the definition of a function.

Question 5

Solve the problem.
-The function $\mathrm { P } ( \mathrm { x } ) = 0.35 \mathrm { x } - 74$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes. Find $\mathrm { P } ( 1000 )$, the profit the vendor makes from selling 1000 pretzels.
A) $\$ 926$
B) $\$ 424$
C) $\$ 350$
D) $\$ 276$

Accepted Answer

The answer of Solve the problem.
-The function \(\mathrm { P...

Question 6

Evaluate the function at the given value of the independent variable and simplify.
-$$f ( x ) = \frac { x ^ { 3 } + 3 } { x ^ { 2 } - 5 } ; \quad f ( 5 )$$
A) $\frac { 128 } { 25 }$
B) $\frac { 32 } { 5 }$
C) $\frac { 7 } { 5 }$
D) $\frac { 25 } { 4 }$

Accepted Answer

To evaluate $f(5)$, substitute $x = 5$ into the function: $f(5) = \frac{5^3 + 3}{5^2 - 5} = \frac{125 + 3}{25 - 5} = \frac{128}{20} = \frac{32}{5}$.

Question 7

Evaluate the function at the given value of the independent variable and simplify.
-$$f ( x ) = \frac { x ^ { 2 } + 6 } { x ^ { 3 } - 5 x } ; \quad f ( - 4 )$$
A) $- \frac { 1 } { 2 }$
B) $- \frac { 4 } { 11 }$
C) $- \frac { 11 } { 32 }$
D) $- \frac { 22 } { 69 }$

Accepted Answer

Explanation:Substitute -4 for x in the function.$$f(-4) = \frac{(-4)^2 + 6}{(-4)^3 - 5(-4)}$$$$= \frac{16 + 6}{-64 + 20}$$$$= \frac{22}{-44}$$$$= -\frac{1}{2}$$

Question 8

Solve the problem.
-The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the function C(x)= 0.8x + 40,000. Find C(50,000), the cost of producing 50,000 jars.
A)$40.80
B)$80,000
C)$40,000
D)$50,040

Accepted Answer

To find C(50,000), substitute x = 50,000 into the function: C(50,000) = 0.8(50,000) + 40,000 = 40,000 + 40,000 = $80,000.

Question 9

Evaluate the function at the given value of the independent variable and simplify.
-$$g ( x ) = 3 x + 1 ; \quad g ( x + 1 )$$
A) $3 x + 4$
B) $3 x - 1$
C) $3 x + 1$
D) $\frac { 1 } { 3 } x + 1$

Accepted Answer

To find $g(x + 1)$, substitute $x + 1$ for $x$ in the function $g(x) = 3x + 1$. This gives $g(x + 1) = 3(x + 1) + 1 = 3x + 3 + 1 = 3x + 4$.

Question 10

Evaluate the function at the given value of the independent variable and simplify.
-$f ( x ) = 3 x ^ { 2 } - 3 x - 4 ; \quad f ( x - 1 )$
A) $- 9 x ^ { 2 } + 3 x + 2$
B) $3 x ^ { 2 } - 15 x - 4$
C) $3 x ^ { 2 } - 9 x - 4$
D) $3 x ^ { 2 } - 9 x + 2$

Accepted Answer

To find $f(x-1)$, substitute $x-1$ for $x$ in the function: $f(x-1) = 3(x-1)^2 - 3(x-1) - 4$. Simplify this expression to get $3x^2 - 9x + 2$.

Question 11

Evaluate the function at the given value of the independent variable and simplify.
-$$h ( x ) = | x - 15 | ; \quad h ( 20 )$$
A) $- 35$
B) 5
C) $- 5$
D) 35

Accepted Answer

The function $h(x) = |x - 15|$ evaluated at $x = 20$ gives $|20 - 15| = |5| = 5$. Absolute value makes the result non-negative.

Question 12

Determine whether the equation defines y as a function of x.
-$$x + y ^ { 2 } = 4$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

For a given value of $x$, there can be two different values of $y$ that satisfy the equation $x + y^2 = 4$, because squaring a number gives a positive result whether the original number is positive or negative. This means that for some values of $x$, there are two corresponding values of $y$, which violates the definition of a function where each input should have exactly one output.

Question 13

Determine whether the equation defines y as a function of x.
-$$y ^ { 2 } = 5 x$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

The equation $y^2 = 5x$ does not define $y$ as a function of $x$ because for any given value of $x$, there are two possible values of $y$ (one positive and one negative) that satisfy the equation. This violates the definition of a function, which requires that each input is associated with exactly one output.

Question 14

Evaluate the function at the given value of the independent variable and simplify.
-$$f ( x ) = - 5 x + 1 ; \quad f ( - 3 )$$
A) 16
B) 12
C) $- 4$
D) 14

Accepted Answer

Substituting $x = -3$ into the function $f(x) = -5x + 1$, we get $f(-3) = -5(-3) + 1 = 15 + 1 = 16$.

Question 15

Determine whether the equation defines y as a function of x.
-$$x y + 9 y = 1$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

To determine if $y$ is a function of $x$, we need to see if for each $x$, there is exactly one $y$. We can solve the equation for $y$ in terms of $x$: $xy + 9y = 1 \Rightarrow y(x + 9) = 1 \Rightarrow y = \frac{1}{x + 9}$. This equation defines $y$ as a function of $x$ because for each $x$, there is exactly one $y$, except when $x = -9$ (which would make the denominator zero, but this is a restriction, not a violation of the function definition).

Question 16

Determine whether the equation defines y as a function of x.
-$$x ^ { 2 } + y ^ { 2 } = 9$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

The equation $x^2 + y^2 = 9$ represents a circle with radius 3 centered at the origin. For some values of $x$, there are two different $y$ values (one positive and one negative) that satisfy the equation. This violates the definition of a function, which requires each input to have exactly one output.

Question 17

Evaluate the function at the given value of the independent variable and simplify.
-$$f ( x ) = \sqrt { x + 6 } ; \quad f ( - 2 )$$
A) $1.41$
B) 2
C) $- 2$
D) not a real number

Accepted Answer

The answer of Evaluate the function at the given value...

Question 18

Determine whether the equation defines y as a function of x.
-$$y = \sqrt { 6 x + 4 }$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

For each value of $x$ that makes the expression under the square root non-negative ($6x + 4 \geq 0$), there is exactly one non-negative output value of $y$, satisfying the definition of a function.

Question 19

Determine whether the equation defines y as a function of x.
-$$| x | - y = 9$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

The equation can be rewritten as $y = |x| - 9$, which defines $y$ as a function of $x$ because for each value of $x$, there is exactly one corresponding value of $y$.

Question 20

Determine whether the equation defines y as a function of x.
-$$y = x ^ { 2 }$$
A) $y$ is a function of $x$
B) $y$ is not a function of $x$

Accepted Answer

For each value of $x$, there is exactly one corresponding value of $y$, satisfying the definition of a function.

Quiz 2: Functions and Graphs

Determine whether the equation defines y as a function of x. - $x = y ^ { 2 }$

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = x ^ { 2 } - 3 ; \quad f ( x - 4 )$

Determine whether the equation defines y as a function of x. - $x + y ^ { 3 } = 27$

Determine whether the equation defines y as a function of x. - $y = - \sqrt { x - 9 }$

Solve the problem. -The function $\mathrm { P } ( \mathrm { x } ) = 0.35 \mathrm { x } - 74$ models the relationship between the number of pretzels $x$ that a certain vendor sells and the profit the vendor makes. Find $\mathrm { P } ( 1000 )$ , the profit the vendor makes from selling 1000 pretzels.

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = \frac { x ^ { 3 } + 3 } { x ^ { 2 } - 5 } ; \quad f ( 5 )$

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = \frac { x ^ { 2 } + 6 } { x ^ { 3 } - 5 x } ; \quad f ( - 4 )$

Solve the problem. -The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the function C(x) = 0.8x + 40,000. Find C(50,000) , the cost of producing 50,000 jars.

Evaluate the function at the given value of the independent variable and simplify. - $g ( x ) = 3 x + 1 ; \quad g ( x + 1 )$

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = 3 x ^ { 2 } - 3 x - 4 ; \quad f ( x - 1 )$

Evaluate the function at the given value of the independent variable and simplify. - $h ( x ) = | x - 15 | ; \quad h ( 20 )$

Determine whether the equation defines y as a function of x. - $x + y ^ { 2 } = 4$

Determine whether the equation defines y as a function of x. - $y ^ { 2 } = 5 x$

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = - 5 x + 1 ; \quad f ( - 3 )$

Determine whether the equation defines y as a function of x. - $x y + 9 y = 1$

Determine whether the equation defines y as a function of x. - $x ^ { 2 } + y ^ { 2 } = 9$

Evaluate the function at the given value of the independent variable and simplify. - $f ( x ) = \sqrt { x + 6 } ; \quad f ( - 2 )$

Determine whether the equation defines y as a function of x. - $y = \sqrt { 6 x + 4 }$

Determine whether the equation defines y as a function of x. - $| x | - y = 9$

Determine whether the equation defines y as a function of x. - $y = x ^ { 2 }$

Quiz 2: Functions and Graphs

Determine whether the equation defines y as a function of x. - x=y2x = y ^ { 2 }x=y2

Evaluate the function at the given value of the independent variable and simplify. - f(x) =x2−3;f(x−4) f ( x ) = x ^ { 2 } - 3 ; \quad f ( x - 4 ) f(x) =x2−3;f(x−4)

Determine whether the equation defines y as a function of x. - x+y3=27x + y ^ { 3 } = 27x+y3=27

Determine whether the equation defines y as a function of x. - y=−x−9y = - \sqrt { x - 9 }y=−x−9​

Evaluate the function at the given value of the independent variable and simplify. - f(x) =x3+3x2−5;f(5) f ( x ) = \frac { x ^ { 3 } + 3 } { x ^ { 2 } - 5 } ; \quad f ( 5 ) f(x) =x2−5x3+3​;f(5)

Evaluate the function at the given value of the independent variable and simplify. - f(x) =x2+6x3−5x;f(−4) f ( x ) = \frac { x ^ { 2 } + 6 } { x ^ { 3 } - 5 x } ; \quad f ( - 4 ) f(x) =x3−5xx2+6​;f(−4)

Solve the problem. -The total cost in dollars for a certain company to produce x empty jars to be used by a jelly producer is given by the function C(x) = 0.8x + 40,000. Find C(50,000) , the cost of producing 50,000 jars.

Evaluate the function at the given value of the independent variable and simplify. - g(x) =3x+1;g(x+1) g ( x ) = 3 x + 1 ; \quad g ( x + 1 ) g(x) =3x+1;g(x+1)

Evaluate the function at the given value of the independent variable and simplify. - f(x) =3x2−3x−4;f(x−1) f ( x ) = 3 x ^ { 2 } - 3 x - 4 ; \quad f ( x - 1 ) f(x) =3x2−3x−4;f(x−1)

Evaluate the function at the given value of the independent variable and simplify. - h(x) =∣x−15∣;h(20) h ( x ) = | x - 15 | ; \quad h ( 20 ) h(x) =∣x−15∣;h(20)

Determine whether the equation defines y as a function of x. - x+y2=4x + y ^ { 2 } = 4x+y2=4

Determine whether the equation defines y as a function of x. - y2=5xy ^ { 2 } = 5 xy2=5x

Evaluate the function at the given value of the independent variable and simplify. - f(x) =−5x+1;f(−3) f ( x ) = - 5 x + 1 ; \quad f ( - 3 ) f(x) =−5x+1;f(−3)

Determine whether the equation defines y as a function of x. - xy+9y=1x y + 9 y = 1xy+9y=1

Determine whether the equation defines y as a function of x. - x2+y2=9x ^ { 2 } + y ^ { 2 } = 9x2+y2=9

Evaluate the function at the given value of the independent variable and simplify. - f(x) =x+6;f(−2) f ( x ) = \sqrt { x + 6 } ; \quad f ( - 2 ) f(x) =x+6​;f(−2)

Determine whether the equation defines y as a function of x. - y=6x+4y = \sqrt { 6 x + 4 }y=6x+4​

Determine whether the equation defines y as a function of x. - ∣x∣−y=9| x | - y = 9∣x∣−y=9

Determine whether the equation defines y as a function of x. - y=x2y = x ^ { 2 }y=x2